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The Spectra of Semi-Normal Singular Integral Operators
C. R. Putnam
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Source: Crossref
Published: Feb 1, 1970
DOI: 10.4153/cjm-1970-017-7
Open original source ↗Source abstract
Suppose that (1.1) and define the bounded self-adjoint operators H and J on the Hilbert space L 2 (0, 1) by (1.2) the integral being a Cauchy principal value It is seen that (1.3) or, equivalently, (1.4) Since ( Cƒ, ƒ ) = π –1 |( ƒ, ϕ )| 2 ≧ 0, A is semi-normal. (For a discussion of such operators, see [ 4 ].)
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